Tiny Geometries

the mysterious structures latent in the Universe

Free computer wallpaper from plasmator.net. Image available at http://www.plasmator.net/wallpaper/GridBall.jpg

 

Tiny Geometries

 

     …partially inspired by Ray Lynch’s wonderful piece of music “Tiny Geometries” on his album “Deep Breakfast”.

(see, for example, http://www.last.fm/music/Ray+Lynch/_/Tiny+Geometries)

 

 

Tiny geometries,

At existence’s core,

Time and space intermixed,

Seething evermore¹.

With bits of time

And bits of space

No further divisible²

This the secret, this the door,

To wherefores still invisible³.

 

 

Through superposition,

Dawns reality⁴.

The rare near impossible,

The norm, certainty⁵.

Dimensions saved,

Held from collapse

Through time irreversible.

Space of no utility,

Both back and forth traversable⁶.

 

 

In shrunken dimensions

Particles arise⁷

Tremors in loops of string

All structure supplies⁸.

What hidden laws,

What mysteries

Ordain the permissible?

Will we through knowledge glean the Whys,

Or sigh, things inexplicable?

 

 

 

 

©2009, Richard Puetter

All rights reserved.

 

 

 

Notes

 

 

Dear reader, this is another “physics” poem. Sorry, but they appeal to me so much. There are many popular writings that will help those unfamiliar with these topics. Topics covered here are quantum gravity, string theory, and the making of Universes through the superposition of all possible states. There are good articles on Wikipedia on these topics and in the science magazine Scientific American. I am also willing to answer to the best of my ability  questions sent to me via e-mail.

 

Very best regards,

 

Rick

 

 

^[1]The properties of matter are currently thought to be determined by geometric structures in miniscule "folded-dimensions". So, on the microscopic scale, tiny geometries determine all. Time and space always intermix because of special relativity, but on the smallest scales, time can "briefly" run backwards and be reversible (cause and effect need not be time-ordered at least not for short periods), i.e., "effects" can actually precede "causes".

 

^[2]There is a smallest unit of time, the Planck time (roughly 5.4x10^-44 sec), and a smallest unit of space (Planck length, approximately 1.6x10^-33 cm), the distance light travels in a Planck time.

 

^[3]In quantum mechanics time and space are continuous, i.e., there is no smallest unit of either quantity, which is convenient since quantum field equations can then be functions of a continuous coordinate system. However, in quantum gravity, time and space themselves must be quantized. This poses serious problems since now standard tricks cannot be used to write down the field equations as the coordinate system itself is discrete.

 

^[4]Reality is a superposition of all possible states. One approach in trying to understand the properties of our 4-dimensional Universe (I’m referring to 1 time dimension and 3 space dimensions and momentarily ignoring rolled up small dimensions from which matter may be comprised--see note [7]), is to form a superposition of all possible 4-dimensional universes, and then take the average as this should provide a accurate picture of reality.

 

^[5]This is a common tautology in statistical mechanics. Since the average of the superposition of all possible states is the most likely reality (by astronomically large probabilities, i.e., a certainty), the nature of reality reflects the typical state in the ensemble of all possible states. So the norm reflects the average (i.e., reality) and one will never see a reality characteristic of an atypical state.

 

^[6]Studies that try to understand the properties of our 4-dimensional space-time have found that without one of the dimensions (i.e., what we call time) being irreversible, the average of the ensemble of all possible Universes typically collapses to lower dimensional structures.  So it seems that one of the only ways quantum mechanically to build a 4-dimensional universe is to have one of the dimensions irreversible, e.g., one can only go forward and not back in this dimension, just like we have with time. Indeed, this may be the single, most important property that distinguishes space and time. In space, you can go back and forth. In time, you cannot.

 

^[7]In modern string theory the particles of matter are made up of strings that live in “folded-up” dimensions, i.e., dimensions that are microscopically small and which have not participated in the expansion of the Universe as have our more familiar 3 spatial dimensions.

 

^[8]Vibrations in the string structures of string theory and the geometric properties of these strings are now thought to give rise to all of the different families of fundamental particles.

Author's Note

6-5-6-5-4-4-7-7-8 meter, abcbdefbf rhyme, with f repeating identically in all three verses. Yep, pretty complicated, just like Nature.

I will answer manyantler's questions here since I think there will be others interested in the answers as well.

First, I'd like to comment on Zeta-Reticuli, which is a double star (binary) system in our galaxy. It is not a galaxy of it's own. Galaxies have hundreds of millions to tens of billions of stars. So a two-star system doesn't qualify as a galaxy. Also, binary star systems are very common. Single stars, like our sun, are in the minority. Double stars, triple stars, quadruple star, etc. happen all the time. When star systems form, the massive systems generally form more than one star. When the system isn't massive enough to form multiple stars, solar systems form out of what's left over. So it is thought that lower mass stars, like our sun, will generally be found with solar systems (planets). In the more massive systems, those with multiple stars, any planets in solar systems are likely to be thrown out of the system by gravitational interaction with the stars of the system. So these would most likely not have planets except way out, past the orbits of the multiple star systems (in such systems the multiple stars orbit around each other).

Now as to how we know the age of our sun, that is rather simple actually. Scientist have extremely good models of stellar structure and stellar evolution. We can predict from first principles all of the different kinds of stars that we see in the sky. We know how massive they are, how hot they are, and how long they live before they turn into a supernova. Extensive observations of clusters of stars can see all of the different kind of stars and can see that the more massive stars have already turned off of the main sequence (this is when stars burn hydrogen in their cores) and have gone into the red-giant phase. This is exactly as predicted by our models and we can use this to date the age of globular clusters (large groupings of stars that have all formed at roughly same time). This precise agreement with theory gives great confidence that we know what is going on in stars. We can also look at the heavy elements produced in stars in their normal burning cycle and in the supernovae phase. This, too, agrees with theory and is another check that we have it right. So from all of this we know that our sun is roughly 5 billion years old. This also agrees well with our independent dating of the age of the earth at roughtly 4.5 billion years old. So this is yet another independent check that we understand the structure and evolutionn of stars. So in another 5 billion years our sun will also turn off the main sequence (it will have exhausted all the hydrogen in its core) and begin to expand and become a red-giant, engulfing the earth (our orbital distance will actually be inside the sun). However before that happens, in about 2-3 billion years, our galaxy, the Milky Way, will have collided with Andromeda, the other large galaxy in our local group of about 20 or so galaxies. This collision will probably knock the sun out of its orbit in our galaxy, but it would probably be too weak to strip off the planets from the sun (at least the inner planets). The collision will be generally disruptive of the galaxy and as the stars from each of the two colliding galaxies coalesce, a new, combined, bigger galaxy will form. From observations, astronomers can see that this is a common occurance in the Universe. Galaxies collide all the time and it is an extremely violent event.

Reviews

[Greg Close]

Rick - really like the style and love the topic. Nothing like a poem about subatomic particles to get my juices flowing. This actually reminded me of a Rush lyric by Neil Peart for the song Natural Science (Permanent Waves, rel. 1980). For no particular reason, just in general flow of the rhythm and the deft but accessible scientific bent of the subject matter.

[Nancy Lee Shrader]

Congrats on your great First Place Winning Poem.

[Fabian G. Franklin]

I like the references drawn in the piece. Very interesting. I'm remided of a genius in the field of molecular physics who went around during the last years of his life wearing gigantic boots so he wouldn't fall through his "solid" floor. Festus said to St. Paul in the New Testament, "Much learning doth make thee mad" lol So it was with the physicist. This also reminded me a bit of a piece of my own writing called Patchwork. I think you'd like it. It covers much of the same subject matter but in very different fashion. When one comes to understand that "reality" is very shaky ground, how can one trust one's own senses? If I told someone they saw everything upside down and there was no color but only different reflections in wavelengths of white light, they would think me quite mad as well, even though it is true. Perception is truth to the fellow who trusts that "seeing is believing". But science declares no absolute truth, only theories and hypothesis. So we have the "Big Bang" theory, the "string" theory, the "theory of evolution" etcetera. But I have found it harder to sway the faith of a child than a mind that has been college educated. What worth does science put on faith? Carl Jung said he did not "believe" anything. I always love a piece of writing that makes me think like this one. I find great joy in mental exercise. I think that is probably the reason that many become scientists.

[Salvatore Buttaci]

Congratulations for winning the time contest!

[deeps]

I am really envious of you!
I wish I had your style but then again I wouldn't be unique.
You know what you are writing and studying.

This once again is amazing. I am glad I started reading your stuff.
You seem very educated. This is really amazing really!
I was never really good at science or mathematics.

But I really found this interesting and worth the lesson.

[Mason Vail]

=D

[Kerry]

You said this poem is about physics, but physics, like other sciences, can easily explain life. I see this piece as more of a metaphor. It is lovely work. I enjoy physics as I am an animator. At the very least I have understand things like particle flow and how objects move not only through space, but through time. Then again, I may be speaking about applied physics? At any rate, this is a wonderful write. The footnotes are equally engaging. You remind me of an astrophysicist who teaches at my college. I could listen to him lecture for days! Thanks for the great write!

By the way, was the image that accompanies the poem created in Bryce? That looks like a Bryce creation.

[Snuggles McClintock]

addendum to previous review: i knew poem good when first i seen the tiny numbers indicatin an exposition on that concept layin near the bottom of page. you sentences good write. onward :)

[Snuggles McClintock]

you had me at footnotes.

[Anthony M Smith Jr]

Excellent poem! From the "Theory of Everything" to "The Atom" has become my hobby! Protons(Greek word for first) with a positive electrical charge and the nuetron(non-electrical proton) which is held together by a strong nuclear force(the most powerful known gravity force) inside a atom. Each atom is like a tiny solar system! The key to the universe.(One followed by 70 zero's the number of atoms in the known universe) I did not know that the atom's come in 92 different elements.
If I had a wish I would become a trans-dimensional being and travel to the edge of the universe some 6 trillion miles away from home(earth) by folding space like closing my cheap telescope and look back in time to where I started! Like a "Impeccable Warrior" never retreat!
Thanks for your words and meanings for they have focused my attention to find the first star or sun that come into being.
My question to you my friend is how do they know our sun(G-0, yellow-orange dwarf star) is old as it is before it collapses into itself? Plus information on the "Zeta-Reticuli Galaxy" and its two binary suns(Zeta 1 and Zeta 2) which is 39 light years from home?
TT-TTO-NI-K
Elk

[Marie Anzalone]

What a truly fun and inspired read! I will have to read them all! It is rare skill to write about quantum physics and make it accessible, interesting, and relevant! I liked the way you posed big questions, and juxtaposed them with the behavior of subatomic particles.

That secret, invisible door- the one where time and space cease to be apart- I cannot help but wonder sometimes if the mystics are the only ones who can enter that door for any long period of time? If so, I believe our greatest scientists are modern day Teresa's of Avalon, and only those in the throes of truest love find more earthly bliss.

I don;t think we'll ever know it all, Rick- what would be the point? Every time we learn something new, we realize how many doors it opens to other questions.

Beautiful write, my new friend. I will be pondering your words for much time. Thanks for sharing!